%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV494^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:35 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 25 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 217 ( 9 ~; 3 |; 2 &; 196 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 22 ( 0 ^; 20 !; 2 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_3,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_4,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_5,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_6,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
sK0: 'type/nums/num' ).
thf(func_def_12,type,
sK1: 'type/nums/num' ).
thf(func_def_13,type,
sK2: 'type/nums/num' ).
thf(f1,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_') ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X1 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_RREC_') ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_REC_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X1 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ X1 )
= $true )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) )
| ( ( 'const/arith/<=' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f10,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) )
& ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) )
& ( $true
= ( 'const/arith/<=' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
inference(cnf_transformation,[],[f1]) ).
thf(f13,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( $true
= ( 'const/arith/<=' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f48,plain,
( ( $true != $true )
| ( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f13,f14]) ).
thf(f51,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f52,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f51,f12]) ).
thf(f53,plain,
$false,
inference(forward_subsumption_resolution,[],[f52,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV494^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n019.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:53:18 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23 % (957453)Will run a generic schedule for satisfiability detection.
% 0.08/0.23 % (957465)dis+10_1_sil=32000:sp=arity:random_seed=3931506845:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.23 % (957465) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-957453-957465"...
% 0.08/0.23 % (957465)...printing done.
% 0.08/0.23 % (957465)Refutation found. Thanks to Tanya!
% 0.08/0.23 % SZS status Theorem for theBenchmark
% 0.08/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.23 % (957465)------------------------------
% 0.08/0.23 % (957465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.23 % (957465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.23 % (957465)CaDiCaL version: 2.1.3
% 0.08/0.23 % (957465)Termination reason: Refutation
% 0.08/0.23 % (957465)Time elapsed: 0.002 s
% 0.08/0.23 % (957465)Peak memory usage: 12 MB
% 0.08/0.23 % (957465)Instructions burned: 4 (million)
% 0.08/0.23 % (957453)Success in time 0.017 s
% 0.08/0.23 % Vampire exiting
%------------------------------------------------------------------------------